Problem: Solve for $z$, $ \dfrac{z}{5z - 6} = 5$
Multiply both sides of the equation by $5z - 6$ $ z = 5(5z - 6) $ $z = 25z - 30$ $0 = 24z - 30$ $30 = 24z$ $24z = 30$ $z = \dfrac{30}{24}$ Simplify. $z = \dfrac{5}{4}$